What is the derivative of (x^2+2x/(3x+6)) ?

The derivative of (x^2+2x/(3x+6)) is 1/3

What is the first derivative of (x^2+2x/(3x+6)) ?

The first derivative of (x^2+2x/(3x+6)) is 1/3

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\frac{d}{d x} (\frac{x ^{2} + 2 x}{3 x + 6})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 2 x}{3 x + 6})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} + 2 x ) ( 3 x + 6 ) - \frac{d}{d x} ( 3 x + 6 ) ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x) = 2 x + 2

\frac{d}{d x} (3 x + 6) = 3

= \frac{( 2 x + 2 ) ( 3 x + 6 ) - 3 ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}}

Simplify

\frac{( 2 x + 2 ) ( 3 x + 6 ) - 3 ( x ^{2} + 2 x )}{( 3 x + 6 ) ^{2}} : \frac{1}{3}

= \frac{1}{3}

What is the derivative of (x^2+2x/(3x+6)) ?
The derivative of (x^2+2x/(3x+6)) is 1/3
What is the first derivative of (x^2+2x/(3x+6)) ?
The first derivative of (x^2+2x/(3x+6)) is 1/3